Problem: What do the following two equations represent? $-3x+4y = 3$ $9x-12y = -3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x+4y = 3$ $4y = 3x+3$ $y = \dfrac{3}{4}x + \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $9x-12y = -3$ $-12y = -9x-3$ $y = \dfrac{3}{4}x + \dfrac{1}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.